Qinfeng Li

collaborators

3 papers

math.AP2026

A Quantitative Pólya--Szegő Theorem for Tangential Polygons

Changfeng Gui, Yeyao Hu, Qinfeng Li

For a bounded Lipschitz domain $Ω \subset R^{2}$ , let $T (Ω) = \int_{Ω} u_{Ω} d x$ denote its torsional rigidity, where $- Δ u_{Ω} = 1$ in $Ω$ and $u_{Ω} = 0$ on $\partial Ω$ . We prove a quantit…

math.AP2026

Mixed Torsion on Right Triangles and the PÃ³lya--SzegÅ Monotonicity Problem for Regular Polygons

Changfeng Gui, Yeyao Hu, Qinfeng Li +1

Motivated by the polygonal PÃ³lya--SzegÅ conjecture for torsional rigidity, we study two monotonicity problems for torsional rigidity. The first concerns a mixed torsion problem o…

math.AP2026

Monotonicity of the first nonzero Steklov eigenvalue of regular $N$ -gon with fixed perimeter

Zhuo Cheng, Changfeng Gui, Yeyao Hu +2

We study the first nontrivial Steklov eigenvalue of perimeter-normalized regular $N$-gons and show that it is strictly increasing in $N$. The proof mainly relies on an analytic…

A Quantitative Pólya--Szegő Theorem for Tangential Polygons

Mixed Torsion on Right Triangles and the PÃ³lya--SzegÅ Monotonicity Problem for Regular Polygons

Monotonicity of the first nonzero Steklov eigenvalue of regular N-gon with fixed perimeter

Mixed Torsion on Right Triangles and the PÃ³lya--SzegÅ Monotonicity Problem for Regular Polygons

Monotonicity of the first nonzero Steklov eigenvalue of regular $N$ -gon with fixed perimeter